РЕБЯТ ПОЖАЛУЙСТА ПОМОГИТЕ!!!!!!! Решите уравнение: 2sin^2 (x)-8sin(x)cos(x)+7cos^2 (x)=1. Created by maslovae420. algebra-ru

РЕБЯТ ПОЖАЛУЙСТА ПОМОГИТЕ!!!!!!! Решите уравнение: 2sin^2 (x)-8sin(x)cos(x)+7cos...

maslovae420 @maslovae420

August 2022 1 32 Report

РЕБЯТ ПОЖАЛУЙСТА ПОМОГИТЕ!!!!!!!
Решите уравнение:
2sin^2 (x)-8sin(x)cos(x)+7cos^2 (x)=1

Answers & Comments

sedinalana

Verified answer

2sin²x-8sinxcosx+7cos²x-sin²x-cos²x=0/cos²x
tg²x-8tgx+6=0
tgx=a
a²-8a+6=0
D=64-24=40
a1=(8-2√10)/2=4-√10⇒tgx=4-√10⇒x=arctg(4-√10)+πn,n∈z
a2=4+√10⇒tgx=4+√10⇒x=arctg(4+√10)+πn,n∈z

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